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Spatial Unit Roots and Spurious Regression

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  • Ulrich K. Müller
  • Mark W. Watson

Abstract

This paper proposes a model for, and investigates the consequences of, strong spatial dependence in economic variables. Our findings echo those of the corresponding “unit root” time series literature: Spatial unit root processes induce spuriously significant regression results, even with clustered standard errors or spatial HAC corrections. We develop large‐sample valid unit root and stationarity tests that can detect such strong spatial dependence. Finally, we use simulations to study strategies for valid inference in regressions with persistent spatial data, such as spatial analogues of first‐differencing transformations. Regressions from Chetty, Hendren, Kline, and Saez (2014) are used to illustrate the issues and methods.

Suggested Citation

  • Ulrich K. Müller & Mark W. Watson, 2024. "Spatial Unit Roots and Spurious Regression," Econometrica, Econometric Society, vol. 92(5), pages 1661-1695, September.
    • Handle: RePEc:wly:emetrp:v:92:y:2024:i:5:p:1661-1695
    DOI: 10.3982/ECTA21654
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    References listed on IDEAS

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    1. Wright, Jonathan H, 2000. "Confidence Sets for Cointegrating Coefficients Based on Stationarity Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 211-222, April.
    2. Lung-Fei Lee & Jihai Yu, 2013. "Near Unit Root in the Spatial Autoregressive Model," Spatial Economic Analysis, Taylor & Francis Journals, vol. 8(3), pages 314-351, September.
    3. Lung-Fei Lee & Jihai Yu, 2009. "Spatial Nonstationarity and Spurious Regression: the Case with a Row-normalized Spatial Weights Matrix," Spatial Economic Analysis, Taylor & Francis Journals, vol. 4(3), pages 301-327.
    4. Ulrich K. Müller & Mark W. Watson, 2023. "Spatial Correlation Robust Inference in Linear Regression and Panel Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(4), pages 1050-1064, October.
    5. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
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    7. Stock, James H., 1991. "Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series," Journal of Monetary Economics, Elsevier, vol. 28(3), pages 435-459, December.
    8. Rossi, Francesca & Lieberman, Offer, 2023. "Spatial autoregressions with an extended parameter space and similarity-based weights," Journal of Econometrics, Elsevier, vol. 235(2), pages 1770-1798.
    9. Elliott, Graham, 1999. "Efficient Tests for a Unit Root When the Initial Observation Is Drawn from Its Unconditional Distribution," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(3), pages 767-783, August.
    10. Hansen, Bruce E. & Lee, Seojeong, 2019. "Asymptotic theory for clustered samples," Journal of Econometrics, Elsevier, vol. 210(2), pages 268-290.
    11. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
    12. Kelly, Morgan, 2019. "The Standard Errors of Persistence," CEPR Discussion Papers 13783, C.E.P.R. Discussion Papers.
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    Cited by:

    1. Richard K. Crump & Nikolay Gospodinov & Ignacio Lopez Gaffney, 2024. "A Jackknife Variance Estimator for Panel Regressions," Staff Reports 1133, Federal Reserve Bank of New York.
    2. Richard K. Crump & Nikolay Gospodinov & Ignacio Lopez Gaffney, 2024. "A Simple Diagnostic for Time-Series and Panel-Data Regressions," Staff Reports 1132, Federal Reserve Bank of New York.

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